Physics 178/278 - The biophysical basis of neurons and networks

(Truth is much too complicated to allow anything but approximations.*)

Course overview

This course explores the cellular and synaptic basis for neuronal control of animal behavior. The emphasis in on
analytically tractable models of network dynamics and neuronal computation. We provide a path from the dynamics of single neurons to three
forms of network activity, each of which involves models where the description of a neuron is reduced to a single
state-variable. The first involves networks of weakly coupled neuronal oscillators in which each neuron is rhythmially active and described
by a firing rate and the phase in its limit cycle, while the interactions depend only on phase differences. These networks provide a natural means to discuss collective dynamics, such as
oscillations and waves in networks of inhibitory neurons. The second and third forms of activity involve circuits of
asynchronous neurons in which each cell is described by a Poisson firing rate and synaptic currents. Recurrent architectures provide a
natural means to discuss attractor-based circuits for motor control, sensory processing and memory. Feedfoward
architectures provide a means to formalize the logic of both single cells with large dendritic fields and motivate
the concept of receptive fields. Both architectures provide design rules to determine connections in terms of the
desired output state(s). Aspects of applied mathematics and experimental procedures are discussed as needed.

There is no offical textbook for the class, although detailed lecture notes are provided for all of the relevant derivations,
long with accompanying graphics from relevant experimental papers.
A fraction of the underlying mathematics is covered in the excellent textbook
"Foundations of Mathematical Neuroscience" by Bard Ermentrout and David Therman (9.2 Mb PDF).

The class meets in room 2702 Mayer Hall in Winter 2020. Lectures are every Tuesday and Thursday from 8:00 to 9:20 AM.
Ms. Mendy Hsu and Mr. Huanqiu Zhang, the class teaching assistants,
will run a discussion section from 6:00 to 7:20 PM every Tuesday on 2702 Mayer Hall. This will include pedagogical material and homework review. Office hours with Ms. Hsu and Mr. Zhang
are 9:30 to 10:30 AM in room 2218 Mayer Hall (enter from plaza) on both Tuesday sand Thursdays and by appointment. Mr. Pantong Yao will
further assist with the preparation of homework and class notes.